Generalized Implicit Multi Time Step Integration for Nonlinear Dynamic Analysis

Abstract

Abstract. This paper deals with a generalized multi-time-step integration used for structural dynamic analysis. The proposed method presents three kinds of implicit schemes in which the accelerations and velocities of the previous steps are utilized to integrate the equations of motion. This procedure employs three groups of weighted factors calculated by minimizing the numerical errors of displacement and velocity in Taylor series expansion. Moreover, a comprehensive study on mathematical stability of the proposed technique, which is performed based on the ampli cation matrices, proves that the new method is more stable than existing schemes such as IHOA. For numerical veri cation, a wide range of dynamic systems, including linear and nonlinear, single and multi degrees of freedom, damped and undamped, as well as forced and free vibrations from nite-element and nitedi erence methods, are analyzed. These numerical studies demonstrate that e ciency and accuracy of the proposed method are higher than those of other techniques.

A Class of Synchronized Nonlinear Two-Dof Systems With Closed Form Solution

“…Studying nonlinear structural dynamic behavior and analysis from di erent theoretical and practical points of view started about a century ago [23][24][25] and have continued more intensively over the last decades [26][27][28][29][30][31][32][33][34][35][36][37][38] and, particularly, the last years [39][40][41][42][43].…”